Mean-field theory for Josephson junction arrays with charge frustration

We derive, using a finite-temperature path integral approach, the equation for the phase boundary between the insulating and the superconducting phase for quantum Josephson junctions arrays (JJA's) with offset charges and gen eral capacitance matrices. We show that-within the mean field theory approx imation-a reentrance in the phase boundary should appear, for systems with a uniform distribution of offset charges, only when the capacitance matrix is nondiagonal. For a model with nearest-neighbor capacitance matrix and un iform offset charge q/2e=112, we find reentrant superconductivity even if t he intergrain interaction is short ranged; for this model, we determine the most relevant contributions to the equations for the phose boundary by exp licitly constructing the charge distributions on the lattice corresponding to the lowest-energy states which provide the leading contributions to the partition function at low T-c.